THE HISTORY AND. SHAPE OF THE TEST-PIECE. 339 broken area could be made only by the most careful duplicate readings and by the aid of the calculus. The variations in elongation may be partially accounted for by unlike methods of measurement,, for if the original punch-marks be put on the outer edge of the bar, they will give a different reading after fracture than if they were, put in the center line, owing to the unequal distortion of the bar. This complication would not occur in a round test-piece. The differences in ultimate strength and elastic limit are due in some measure to slight variations in the original measurements of the bar. The elastic limit was found by noting the "drop of 'the beam," this being the universal practice in"' American steel works and rolling mills. The statement that this method is especially inaccurate is open to debate. In Table XVI- V the elongation, as determined by different observers, varies from 29.50 to 31.46 per cent., these figures being in the ratio of 100 to 106.6, or a range of error of 6.6 per,. cent. The reduction of area varies from 53.8 to 61.6 per cent., a ratio of 100 to 114.5, or a range of error of 14.5 per cent. The elastic ratio varies from 63. 2 to 69.1 per cent., a ratio of 100 to 109.3, or a range of error of 9.3 per cent. Thus the determination of the elastic ratio is much more accurate than the results on contraction of area, and nearly as accurate as the results on elongation, both determined by exact measurements made on the piece when at rest. It would be in order for reformers to apply their energies to the accurate determination of the reduction of area and the elongation, instead of trying to substitute a new method for determining the elastic limit, especially when this method has been: publicly branded as inaccurate.* ' • As a rule, the autographic device gives a slightly lower reading. than the drop of the beam; thus Gus. C. Henningf gives the determinations of the elastic limit on a series of tests, as found by the'*: two methods. I have averaged the list of heats where both read-1 ings are given, and in thirty-eight cases the autographic record was 46.6 per cent. of. the ultimate strength, while the beam dropped' at 52.9 per cent.; in the annealed bar the first method gave 51.6 per cent., and the second 56.9 per cent. Such, a marked difference is not found in all cases, as shown by Table X"V]I-"W, which gives1 the; , ., Tr.an8.Am.Soc. Civil JSng. Vol. XXXIII, p. 351. "t Trans. Ani.Soc. Mech. Engn Vol. XIII, p. 572.